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CATEGORIES:Isaac Newton Institute Seminar Series
SUMMARY:Khintchine types of translated coordinate hyperpla
nes - Ramirez\, F (University of York)
DTSTART;TZID=Europe/London:20140623T113000
DTEND;TZID=Europe/London:20140623T123000
UID:TALK53070AThttp://talks.cam.ac.uk
URL:http://talks.cam.ac.uk/talk/index/53070
DESCRIPTION:This talk is about the problem of simultaneously a
pproximating a tuple of real numbers by rationals\
, when one of the real numbers has been prescribed
. This corresponds to describing the set of ration
ally approximable points on translates of coordina
te hyperplanes in Euclidean space. It is expected
that under a divergence condition on the desired r
ate of approximation\, we should be able to assert
that almost every point on the hyperplane is rati
onally approximable at that rate\, like in Khintch
ine's Theorem. We will discuss some positive resul
ts in this direction. These can be seen as living
in the degenerate counterpart to work of Beresnevi
ch and Beresnevich--Dickinson--Velani\, where simi
lar results were achieved for non-degenerate subma
nifolds of Euclidean space.\n
LOCATION:Seminar Room 2\, Newton Institute Gatehouse
CONTACT:Mustapha Amrani
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